Under the provisions of the Access to Neighbouring Land Act 1992, s1(1), if the neighbour will not give you consent to enter in the land for any work reasonably required to preserve your property (that means maintain it and this would certainly be maintenance) then you can apply to court for an order against the neighbour and you can ask the court to award the legal costs against him.
Here is the statutory provision. It is a very short act and quite self-explanatory. http://www.legislation.gov.uk/ukpga/1992/23/contents
Tell the neighbour in writing that unless he/she gives access to you in order to be able to carry out this maintenance and to do so within the next 7 days, you will make an application to court for a court order without further notice. A solicitors letter will probably carry more weight. The neighbour cannot continue to refuse access for this purpose.
Please note that you are not allowed access under this act for new building although you are allowed access for new building under the Party Wall Act.
As this is their foliage, you have a claim against them in common law nuisance and a claim against them in negligence for allowing this to happen although, if you were aware it was happening yourself and didn’t know anything about it, it may reduce your claim because you did not make any attempts to mitigate your loss.
Check your house insurance as many house insurance policies have legal expenses cover that may pay for the legal costs.
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